Question

If u +t=5 and u-t =2, what is the value of (u-t)(u^2 -t^2) *20O 15O 2025O 30

Answer 1

The value of (u - t)(u^2 - t^2) is 30. To find the value of (u - t)(u^2 - t^2), first, recognize the equations provided: u + t = 5 and u - t = 2. Using these equations, solve for u and t separately.

Step-by-step explanation:

Given u + t = 5 and u - t = 2, we can solve these equations simultaneously to find the values of u and t. Adding the equations together eliminates t: (u + t) + (u - t) = 5 + 2, which simplifies to 2u = 7, and u = 7/2. Subtracting the second equation from the first eliminates u: (u + t) - (u - t) = 5 - 2, simplifying to 2t = 3, and t = 3/2.

Now that we have the values of u and t, we can find (u^2 - t^2). Substitute u = 7/2 and t = 3/2 into the equation to get (u^2 - t^2) = (7/2)^2 - (3/2)^2 = 49/4 - 9/4 = 40/4 = 10.

Finally, multiply (u - t) by (u^2 - t^2): (u - t)(u^2 - t^2) = (2)(10) = 20.

Therefore, the value of (u - t)(u^2 - t^2) is 20.

Answer 2

The value of the expression is 1/5.

Step-by-step explanation:

The first step to solve this question is finding the values of u and t, solving the system.

u + t = 5

u - t = 2

Adding the two lines:

u + u + t - t = 5 + 2

2u = 7

u = 7/2

t = 5 - u = 5 - (7/2) = (10/2) - (7/2) = 3/2

Now we find the value of the expression:

`(u-t)/(u^2-t^2)=((7)/(2)-(3)/(2))/(((7)/(2))^2-((3)/(2))^2)=((4)/(2))/((49)/(4)-(9)/(4))=(2)/((40)/(4))=(2)/(10)=(1)/(5)`

The value of the expression is 1/5.